On Tao's blog, guest authors say OpenAI's Navier-Stokes result is an answer, not a proof math can use

On Tao's blog, guest authors say OpenAI's Navier-Stokes result is an answer, not a proof math can use

  • Guest post by Silvia De Toffoli (IUSS Pavia) and Eamon Duede (Princeton, Purdue) on Terence Tao's blog argues that OpenAI's September 8, 2026 Navier-Stokes announcement is an answer, not a solved problem, because the Lean formalization secures logical certainty without giving mathematicians an intelligible proof they can understand and build on.
  • The post splits proof into two notions: the logical one, where a mechanical checker verifies deductive validity, and the intelligible one, where mathematicians grasp why a proposition is true and connect it to existing knowledge, citing Thurston 1994 for the second.
  • Tristan Buckmaster, a mathematician involved in the Navier-Stokes work, called the result a "Deep Blue-Kasparov moment" in his statement, a framing the authors reject by rejecting the idea that mathematics is a game with winning as its point.
  • The authors name two assumptions behind the "AI solved mathematics" narrative, that AI really solved a math problem and that mathematics is only about solving problems, and say both are wrong, pointing to concept building, unification, teaching, and beauty as parts of the enterprise.
  • Commenters point to an open letter at mathandai.org signed by 25 Fields Medalists and more than 5,000 mathematicians, a separate petition with over 1,900 signatures about the Caltech Mathathon, and public concerns from Fields Medalist James Maynard.

Hacker News opinions

Feels like things changed overnight. 25 Fields Medalists and 5000+ mathematicians from top institutions signed an open letter at mathandai.org about AI's impact on math, and 1900+ signed concerns over the Caltech Mathathon. Maynard has spoken out too.

The proof part isn't the real issue, attribution is. OpenAI took the last tiny step, but it can't credit the mathematicians whose chat logs from the past few months were fed into its training data. I can still remember which exposition sank in for me a decade after grad school; an LLM can't even remember where it learned things.

That reading misses the point. Millennium problems weren't picked for absolute difficulty, they were picked because a proof had a good chance of producing fruitful new concepts and theories. Chasing truth isn't some subjective number-poetry hobby.

Actually I'd keep the number-poetry. Take a math pursuit without it and with only attribution, calculation and puzzle-solving, and you get largest-prime or furthest-digit-of-pi contests, which feel trivial, more like IFLS Facebook posts than arXiv preprints.

The doom and gloom mostly props up AI company valuations. It's still very unclear how much work OpenAI actually did versus just copying the nearly complete homework of someone who got there five minutes earlier.

Perelman rejected the Fields Medal and the Clay prize over attribution and ethics, and nobody here has mentioned him, in a story about another Clay prize. The observation of deep truths seems to take a toll on people.

Wouldn't AI make math more ambitious? In software it works that way for me, I'll take on tasks now that were too risky in 2025 because it was unclear if they were worth it. Prototype first, then judge what's possible.

Where's the payoff though? The software I actually use looks the same as it did in 2021, and no release from Google or Microsoft in the past six months made me go wow. The vibecoded Show HN projects are half-broken and abandoned. Less commitment, not more ambition.

We need a word for this: purpose death. The existential dread of never reaching self-actualization in a field that just got automated, after years of chasing excellence in it. I went through it as a software engineer, and it's strange watching a prominent figure go through the same grief in public.

That framing hands AI an agency that actually sits with its creators. It's very convenient for them to have people believe nobody controls the thing, like Facebook claiming it isn't a publisher but on steroids.

Small correction, the authors are Silvia De Toffoli and Eamon Duede. Tao hosted the post on his blog, he didn't write it, and he's been pro-AI for years, so the grief-stage read is way off.

Purpose death looks more like a step toward enlightenment to me. Four or five generations of capitalism pushed everyone to define themselves almost entirely by their work, and lifelong curiosity handles automation fine.

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